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With our very limited memories, we provide a brief review of Paul Frampton's memories of the discovery of the Veneziano model, with this indeed being string theory, with Y. Nambu, and, secondly, his 3-3-1 theory. The latter is, indeed, a non-excluded replacement for the Standard Model with triangle anomalies being cancelled, as they must in a truly viable theory. It even needs (essentially) three as the family number! Moreover, primordial black holes as dark matter is mentioned. We end with a review of my own very speculative, utterly recent idea that for the purpose of the classical approximation, we could, using the functional integral as our rudimentary assumption taken over from quantum mechanics, obtain the equations of motion without the, in our opinion, very mysterious imaginary unit i, which usually occurs as a factor in the exponent of the functional integrand, which is this i times the action. The functional integral without the mysterious i leads to the prediction of some of the strongest features in cosmology, and also seems to argue for as few black holes as possible and for the cosmological constant being zero. [ABSTRACT FROM AUTHOR]

We carry on the approach used in [L. Schiavone, The inverse problem within free Electrodynamics and the coisotropic embedding theorem, Inter. J. Geom. Meth. Mod. Phys.21(7) (2024) 2450131] to provide a solution for the inverse problem of the calculus of variations for Maxwell equations in vacuum and we provide an abstract theory including all implicit differential equations that can be formulated in terms of vector fields over pre-symplectic manifolds. [ABSTRACT FROM AUTHOR]

Under certain assumptions and independent of the instantons, we show that the logarithm expansion of dimensional regularization in quantum field theory needs a nonperturbative completion to have a renormalization group flow valid at all energies. Then, we show that such nonperturbative completion has the analytic properties of the renormalons, which we find with only a marginal reference to diagrammatic calculations. We demonstrate that renormalon corrections necessarily lead to analyzable functions, namely, resurgent transseries. A detailed analysis of the resurgent properties of the renormalons is provided. The self-consistency of the theory requires these nonperturbative contributions to render the running coupling well defined at any energy, thus with no Landau pole. We illustrate the point within the case of quantum electrodynamics (QED). This way, we explicitly realize the correspondence between the nonperturbative Landau pole scale and the renormalons. What is seen as a Landau pole in perturbation theory is cured by the nonperturbative, resurgent contributions. [ABSTRACT FROM AUTHOR]

The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms, have received a lot of attention in the literature. However, a full understanding of the relation between them is not available, especially when the gauge theories are defined over regions with boundaries. Here, we consider this issue, by first making it precise what we mean by equivalence between the two formalisms. Then, we explore several first-order gauge theories and assess whether their corresponding descriptions satisfy the notion of equivalence. We shall show that, even when in several cases the two formalisms are indeed equivalent, there are counterexamples that signal that this is not always the case. Thus, non-equivalence is a generic feature of gauge field theories. These results call for a deeper understanding of the subject. [ABSTRACT FROM AUTHOR]

We consider Yang–Mills theory with a compact structure group G on a Lorentzian 4-manifold M = ℝ × Σ such that gauge transformations become identity on a submanifold S of Σ (framing over S ⊂ Σ). The space S is not necessarily a boundary of Σ and can have dimension k ≤ 3. Framing of gauge bundles over S ⊂ Σ demands introduction of a G -valued function ϕ S with support on S and modification of Yang–Mills equations along ℝ × S ⊂ M. The fields ϕ S parametrize non-equivalent flat connections mapped into each other by a dynamical group S changing gauge frames over S. It is shown that the charged condensate ϕ S is the Stueckelberg field generating an effective mass of gluons in the domain S of space Σ and keeping them massless outside S. We argue that the local Stueckelberg field ϕ S can be responsible for color confinement. We also briefly discuss local breaking of symmetries in gravity. It is shown that framing of the tangent bundle over a subspace of spacetime makes gravitons massive in this subspace. [ABSTRACT FROM AUTHOR]

We consider a formalism to describe the false-vacuum decay of a scalar field in gauge theories in non-perturbative regimes. We find that the larger the gauge coupling with respect to the self-coupling of the scalar, the shallower the local minimum of the unstable vacuum, to the point where it disappears. This offers the possibility to obtain a consistent picture of early universe cosmology: at high temperatures, a false-vacuum decay is strongly favored and the universe naturally evolves towards a stable state. [ABSTRACT FROM AUTHOR]

We review some aspects of higher spin symmetry, in (Anti-)de Sitter and flat space–times, aiming at closing the gap between the constantly curved and flat cases. On (Anti-)de Sitter space, non-Abelian higher spin algebras are at the core of the construction of interacting theories of higher spin gravity. By considering a suitable contraction of these algebras, we show that similar considerations can apply to Minkowski space–time. We identify a unique candidate to the role of higher spin symmetry in flat space that can also be built as a quotient of the universal enveloping algebra of the isometries of the vacuum, as in the (Anti-)de Sitter case. We then show how to recover the free dynamics from the gauging of the resulting algebra at the linear level. Finally, we show how to realise this gauge algebra as a subset of the global symmetries of a Carrollian conformal scalar field theory living on the null infinity of Minkowski space–time. This theory emerges as the limit of vanishing speed of light of a free massless relativistic scalar. The identification of the same higher spin algebra that rules the dynamics in the bulk of space–time within the global symmetries of this boundary theory paves the way to a flat counterpart of higher spin holography. [ABSTRACT FROM AUTHOR]

In this work, we propose a parity-invariant Maxwell–Chern–Simons U (1) × U (1) model coupled with two charged scalar fields in 2 + 1 dimensions, and show that it admits finite-energy topological vortices. We describe the main features of the model and find explicit numerical solutions for the equations of motion, considering different sets of parameters and analyzing some interesting particular regimes. We remark that the structure of the theory follows naturally from the requirement of parity invariance, a symmetry that is rarely envisaged in the context of Chern–Simons theories. Another distinctive aspect is that the vortices found here are characterized by two integer numbers. [ABSTRACT FROM AUTHOR]

We present a review of Witten index calculations in different supersymmetric gauge theories in four dimensions: supersymmetric electrodynamics, pure = 1 supersymmetric Yang–Mills (SYM) theories and also SYM theories including matter multiplets — both with chirally symmetric and asymmetric content. [ABSTRACT FROM AUTHOR]

The Hamilton–Jacobi formalism is used to analyze the Weyl theory in the weak-field limit. The complete set of involutive Hamiltonians is obtained, which are classified into involutive and non-involutive. The counting of degrees of freedom is performed. Additionally, the generalized brackets and gauge symmetries are reported. [ABSTRACT FROM AUTHOR]

We develop the BRST–BV approach to the construction of the general off-shell Lorentz covariant cubic, quartic, and -tic interaction vertices for irreducible higher-spin fields on -dimensional Minkowski space. We consider two different cases for interacting integer higher-spin fields with both massless and massive fields. The deformation procedure to find a minimal BRST–BV action for interacting higher-spin fields, defined with help of a generalized Hilbert space, is based on the preservation of the master equation in each power of the coupling constant starting from the Lagrangian formulation for a free gauge theory. For illustration, we consider the construction of local cubic vertices for irreducible massless fields of integer helicities, and massless fields and one massive field of spins . For a triple of two massless scalars and a tensor field of integer spin, the BRST–BV action with cubic interaction is explicitly found. In contrast to the previous results on cubic vertices, following our results for the BRST approach to massless fields, we use a single BRST–BV action instead of the classical action with reducible gauge transformations. The procedure is based on the complete BRST operator that includes the trace constraints used in defining the irreducible representation with a definite integer spin. [ABSTRACT FROM AUTHOR]

In this brief survey, we discuss some of the scientific and philosophical problems and debates that underlie the notions of identity, individuality and indistinguishability in physics and mathematics. We critically analyse the different positions for or against the existence of indistinguishable objects in different scientific theories, notably quantum mechanics and gauge theories in physics and homotopy type theory in mathematics. We argue that the different forms of indistinguishability that occur in many areas of physics and mathematics—far from being a problem to be eradicated—exhibit a rich formal structure that plays a key role in the corresponding theories that needs to be properly understood. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'. [ABSTRACT FROM AUTHOR]

Manifolds with boundary, with corners, b -manifolds and foliations model configuration spaces for particles moving under constraints and can be described as E -manifolds. E -manifolds were introduced in Nest and Tsygan (2001 Asian J. Math. 5 599–635) and investigated in depth in Miranda and Scott (2021 Rev. Mat. Iberoam. 37 1207–24). In this article we explore their physical facets by extending gauge theories to the E -category. Singularities in the configuration space of a classical particle can be described in several new scenarios unveiling their Hamiltonian aspects on an E -symplectic manifold. Following the scheme inaugurated in Weinstein (1978 Lett. Math. Phys. 2 417–20), we show the existence of a universal model for a particle interacting with an E -gauge field. In addition, we generalise the description of phase spaces in Yang–Mills theory as Poisson manifolds and their minimal coupling procedure, as shown in Montgomery (1986 PhD Thesis University of California, Berkeley), for base manifolds endowed with an E -structure. In particular, the reduction at coadjoint orbits and the shifting trick are extended to this framework. We show that Wong's equations, which describe the interaction of a particle with a Yang–Mills field, become Hamiltonian in the E -setting. We formulate the electromagnetic gauge in a Minkowski space relating it to the proper time foliation and we see that our main theorem describes the minimal coupling in physical models such as the compactified black hole. [ABSTRACT FROM AUTHOR]

We review the present status of gauge theories built on various quantum space–times described by noncommutative space–times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory models on Moyal spaces as well as on quantum spaces whose coordinates form a Lie algebra are covered, with particular emphasis on some explored quantum properties. Recent attempts aiming to include gravity dynamics within a noncommutative framework are also considered. [ABSTRACT FROM AUTHOR]

In a (2 + 1) -dimensional Maxwell–Chern–Simons theory coupled with a fermion and a scalar, which has = 2 SUSY in the absence of the boundary, supersymmetry is broken on the insertion of a spatial boundary. We show that only a subset of the boundary conditions allowed by the self-adjointness of the Hamiltonian can preserve partial ( = 1) supersymmetry, while for the remaining boundary conditions SUSY is completely broken. In the latter case, we demonstrate two distinct SUSY-breaking mechanisms. In one scenario, the SUSY-breaking boundary conditions are not consistent with the supersymmetry transformations. In another scenario, despite the boundary conditions being consistent with the SUSY transformations, unpaired fermionic edge states in the domain of the Hamiltonian leads to the breaking of the supersymmetry. [ABSTRACT FROM AUTHOR]

Recently, Dewar (2019) has suggested that one can apply the strategy of 'sophistication'—as exemplified by sophisticated substantivalism as a response to the diffeomorphism invariance of General Relativity—to gauge theories such as electrodynamics. This requires a shift to the formalism of fibre bundles. In this paper, I develop and defend this suggestion. Where my approach differs from previous discussions is that I focus on the metaphysical picture underlying the fibre bundle formalism. In particular, I aim to affirm the physical reality of gauge properties. I argue that this allows for a local and separable explanation of the Aharonov-Bohm effect. Its puzzling features are explained by a form of holism inherent to fibre bundles. [ABSTRACT FROM AUTHOR]

Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is usually presented as a mere recipe of Dirac, with no explanation as to how it works. It then comes to discussing conjectures of whether all primary constraints correspond to gauge symmetries, and it goes all the way to absolutely wrong claims such as the statement that electrodynamics or gravity only have two physical components each, with others being spurious. One has to be very careful because non-dynamical, or constrained, does not mean unphysical. In this article, I give a pedagogical introduction to the degenerate Hamiltonian systems, showing both very simple mechanical examples and general arguments about how it works. For the familiar field theory models, I explain why the gauge freedom there "hits twice" in the sense of producing twice as many first-class constraints as gauge symmetries, and why primary, and only primary, constraints should be put into the total Hamiltonian. [ABSTRACT FROM AUTHOR]

Classical gravity is understood as the geometry of spacetime, and it seems very different from the other known interactions. In this review, I will instead stress the analogies: Like strong interactions, the low energy effective field theory of gravity is related to a nonlinearly realized symmetry, and like electroweak interactions, it is a gauge theory in Higgs phase, with a massive connection. I will also discuss the possibility of finding a UV complete quantum field theoretic description of all interactions. [ABSTRACT FROM AUTHOR]

In this paper, we make a complete revision about Nöther's theorems: The one which refers to the global symmetries, the theorem referring to the local ones, and the corresponding reciprocal theorems. We exemplify these theorems by applying them to a variety of situations. Particularly, we show, through the example of Kepler's problem, that the first reciprocal Nöther's theorem finds its maximal applicability only in the Hamiltonian formalism in which the dynamical symmetries are realizable. Finally, we expose the relation between Nöther's energy-momentum tensor and the metric one. We complement the information by treating, in appendix, Lévy-Leblond-Jackiw's formulation that intends to unify the two theorems. [ABSTRACT FROM AUTHOR]

After many years of investigations, our understanding of the dynamics of strongly coupled chiral gauge theories is still quite unsatisfactory today. Conventional wisdom about strongly coupled gauge theories, successfully applied to QCD, is not always as useful in chiral gauge theories. Recently, some new ideas and techniques have been developed, which involve concepts of generalized symmetries, of gauging a discrete center symmetry, and of generalizing the 't Hooft anomaly matching constraints to include certain mixed symmetries. This new development has been applied to chiral gauge theories, leading to many interesting, sometimes quite unexpected, results. For instance, in the context of generalized Bars–Yankielowicz and generalized Georgi–Glashow models, these new types of anomalies give a rather clear indication in favor of the dynamical Higgs phase, against confining, flavor symmetric vacua. Another closely related topic is strong anomaly and the effective low-energy action representing it. It turns out that they have significant implications on the phase of chiral gauge theories, giving indications consistent with the findings based on the generalized anomalies. Some striking analogies and contrasts between the massless QCD and chiral gauge theories seem to emerge from these discussions. The aim of this work is to review these developments. [ABSTRACT FROM AUTHOR]

In this short note we discuss N-supersymmetric worldlines of relativistic massless particles and review the known result that physical spin-N/2 fields are in the first BRST cohomology group. For N = 1, 2, 4, emphasis is given to particular deformations of the BRST differential, that implement either a covariant derivative for a gauge theory or a metric connection in the target space seen by the particle. In the end, we comment about the possibility of incorporating Ramond-Ramond fluxes in the background. [ABSTRACT FROM AUTHOR]

It is well‐known that gauging a finite 0‐form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0‐form symmetry group which form a 1‐category. We argue that for a d‐dimensional quantum field theory the full set of dual symmetries one obtains is in fact much larger and is described by a (d−1)$(d-1)$‐category, which is formed out of lower‐dimensional topological quantum field theories with the same 0‐form symmetry. We study in detail a 2‐categorical piece of this (d−1)$(d-1)$‐category described by 2d topological quantum field theories with 0‐form symmetry. We further show that the objects of this 2‐category are the recently discussed 2d condensation defects constructed from higher‐gauging of Wilson lines. Similarly, dual symmetries obtained by gauging any higher‐form or higher‐group symmetry also form a (d−1)$(d-1)$‐category formed out of lower‐dimensional topological quantum field theories with that higher‐form or higher‐group symmetry. A particularly interesting case is that of the 2‐category of dual symmetries associated to gauging of finite 2‐group symmetries, as it describes non‐invertible symmetries arising from gauging 0‐form symmetries that act on (d−3)$(d-3)$‐form symmetries. Such non‐invertible symmetries were studied recently in the literature via other methods, and our results not only agree with previous results, but our approach also provides a much simpler way of computing various properties of these non‐invertible symmetries. We describe how our results can be applied to compute non‐invertible symmetries of various classes of gauge theories with continuous disconnected gauge groups in various spacetime dimensions. We also discuss the 2‐category formed by 2d condensation defects in any arbitrary quantum field theory. It is well‐known that gauging a finite 0‐form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0‐form symmetry group which form a 1‐category. Here it will be argued that for a d‐dimensional quantum field theory the full set of dual symmetries one obtains is in fact much larger and is described by a (d − 1)‐category, which is formed out of lower‐dimensional topological quantum field theories with the same 0‐form symmetry. The authors study in detail a 2‐categorical piece of this (d−1)‐category described by 2d topological quantum field theories with 0‐form symmetry. It further will be shown that the objects of this 2‐category are the recently discussed 2d condensation defects constructed from higher‐gauging of Wilson lines. Similarly, dual symmetries obtained by gauging any higher‐form or higher‐group symmetry also form a (d − 1)‐ category formed out of lower‐dimensional topological quantum field theories with that higher‐form or higher‐group symmetry. A particularly interesting case is that of the 2‐category of dual symmetries associated to gauging of finite 2‐group symmetries, as it describes non‐invertible symmetries arising from gauging 0‐form symmetries that act on (d − 3)‐form symmetries. Such non‐invertible symmetries were studied recently in the literature via other methods, and our results not only agree with previous results, but our approach also provides a much simpler way of computing various properties of these non‐invertible symmetries. it will be described how the results obtained here can be applied to compute noninvertible symmetries of various classes of gauge theories with continuous disconnected gauge groups in various spacetime dimensions. Finally there is a discussion of the 2‐category formed by 2d condensation defects in any arbitrary quantum field theory. [ABSTRACT FROM AUTHOR]

We present variational formulations of gauge theories and Einstein–Yang–Mills equations in the spirit of Kaluza–Klein theories. For gauge theories, only a topological fibration is assumed. For gravitation coupled with gauge fields, no fibration is assumed: Fields are defined on a ‘space-time’ Y of dimension 4 + r without any structure a priori, where r is the dimension of the structure group. If the latter is compact and simply connected, classical solutions allow to construct a manifold X of dimension 4 to be the physical space-time, in such a way that Y acquires the structure of a principal bundle over X and leads to solutions of the Einstein–Yang–Mills systems. The special case of the Einstein–Maxwell system is also discussed: It suffices that at least one fiber closes in on a circle to deduce that the five-dimensional space-time has a fiber bundle structure. [ABSTRACT FROM AUTHOR]

Assuming that the geometry of spacetime is uniquely determined by the energy–momentum tensor of matter alone, i.e. without any interactions, enables us to construct the Lagrangian from which the metric of higher dimensional spacetime follows. From the geodesic equations that follow, it becomes clear that the incorrect mass of elementary particles predicted by Kaluza–Klein theories arises from the assumption that in the absence of gravity the solution to the Einstein field equations reduces to the Minkowski metric. From construction of a consistent theory of 4 D electromagnetism, we find that this assumption does not only result in the incorrect mass of elementary particles, but also the incorrect value of the cosmological constant. This suggests that these incorrect predictions, which are often regarded as major flaws of Kaluza–Klein theories, just reflect the inconsistency of the assumption that the solution to Einstein field equations reduces to Minkowski metric in the absence of gravity and Weyl invariance which is the symmetry of gauge theories in 4 D spacetime. Abandoning this assumption results in modification of general relativity. We show that the unified description of fundamental interactions naturally incorporates the Higgs mechanism. For non-Abelian gauge fields, we find that the manifold comprising the extra dimensions has to be a group manifold and show that the standard model is realized in 16 D spacetime. We show that charge and spin are the same concept, but what makes them different is that the former follows from symmetry of 4 D spacetime while the latter follows from symmetry of the internal space. • Kaluza–Klein metric is generally not the solution to vacuum Einstein equations. • Solution to unrealistic mass problem is possible for modified general relativity. • Compactification does not result in infinite tower of massive modes. • Unified description of particles is possible in higher dimensions. [ABSTRACT FROM AUTHOR]

The aim of this work is to discuss and explore some generalized aspects of generation of photon mass respecting gauge symmetry. We introduce generalized Stueckelberg and Higgs gauge theories and present the classical and quantum frameworks related to them. We construct the quantum theory by writing the transition amplitude in the Fadeev-Senjanovic formalism and put it in a covariant form by the Fadeev-Popov method. We also analyse the independence of the transition amplitude by gauge parameters via BRS-T symmetry. Even in the generalized context, the Stueckelberg structure influences the quantization process of the Higgs theory in the ’t Hooft’s fashion, in which an intimate relationship between the Stueckelberg compensating field and the Goldstone boson arises. [ABSTRACT FROM AUTHOR]

We consider Yang–Mills theory with a compact gauge group G on Minkowski space R 3 , 1 and compare the introduction of masses of gauge bosons using the Stueckelberg and Higgs mechanisms. The Stueckelberg field ϕ is identified with a G-frame on the gauge vector bundle E and the kinetic term for ϕ leads to the mass of the gauge bosons. The Stueckelberg mechanism is extended to the Higgs mechanism by adding to the game a scalar field describing rescaling of metric on fibres of E. Thus, we associate Higgs fields as well as running coupling parameters with conformal geometry on fibres of gauge bundles. In particular, a running coupling tending to zero or to infinity is equivalent to an unbounded expansion of G-fibres or its contraction to a point. We also discuss scale connection, space-time dependent Higgs vacua and compactly supported gauge and quark fields as an attribute of confinement. [ABSTRACT FROM AUTHOR]

In this review, we revisit our latest works regarding the description of the gravitational interaction on noncommutative spaces as matrix models. Specifically, inspired by the gauge-theoretic approach of (ordinary) gravity, we make use of the suggested methodology, modified appropriately for the noncommutative framework, of the well-established formulation of gauge theories on them. Making use of a covariant four-dimensional fuzzy space, we formulate the gauge theory with an extended gauge group due to noncommutativity. In turn, in order to decrease the amount of symmetry we employ a symmetry breaking and result with an action which describes a theory that is a minimal noncommutative extension of the original. [ABSTRACT FROM AUTHOR]

In this paper, we study Z N symmetry of S U (N) gauge group, in one-dimensional gauged chain. The action can be obtained by considering the terms of a (3 + 1) -dimensional Euclidean lattice action of a S U (N) gauge theory that break the Z N symmetry explicitly. The matter fields in the resulting partition function can be integrated out exactly, for a given background of link variables, to calculate the Polyakov loop free energy. To keep the temperature fixed, the lattice spacing is scaled appropriately as the number of "temporal" sites is varied. In the case of Higgs as matter field, the Polyakov loop free energy exhibits the Z N symmetry in the limit of large number of temporal sites. For fermions, the strength of Z N explicit breaking decreases for finer lattices, but approaches a nonzero value in the same limit. We discuss the possible implications of these results to S U (N) gauge theories in 3 + 1 dimensions. [ABSTRACT FROM AUTHOR]

The 1.5 formalism played a key role in the discovery of supergravity and it has been used to prove the invariance of essentially all supergravity theories under local supersymmetry. It emerged from the gauging of the super Poincaré group to find supergravity. We review both of these developments as well as the auxiliary fields for simple supergravity and its most general coupling to matter using the tensor calculus. [ABSTRACT FROM AUTHOR]

We recall the well-known description of the conformal gravity as a gauge theory and translate the program to the noncommutative framework by constructing a gravity model on a covariant 4D noncommutative space. After determining the action of the theory we proceed to a symmetry breaking scheme by the imposition of constraints. [ABSTRACT FROM AUTHOR]

The Dirac–Bergmann algorithm is a recipe for converting a theory with a singular Lagrangian into a constrained Hamiltonian system. Constrained Hamiltonian systems include gauge theories—general relativity, electromagnetism, Yang–Mills, string theory, etc. The Dirac–Bergmann algorithm is elegant but at the same time rather complicated. It consists of a large number of logical steps linked together by a subtle chain of reasoning. Examples of the Dirac–Bergmann algorithm found in the literature are designed to isolate and illustrate just one or two of those logical steps. In this paper, I analyze a finite-dimensional system that exhibits all of the major steps in the algorithm. The system includes primary and secondary constraints, first and second class constraints, restrictions on Lagrange multipliers, and both physical and gauge degrees of freedom. This relatively simple system provides a platform for discussing the Dirac conjecture, constructing Dirac brackets, and applying gauge conditions. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of interactions between stationary electromagnetic sources for the minimal and nonminimal CPT-odd photon sector of the Standard Model Extension (SME), where we search mainly for physical phenomena not present in the Maxwell electrodynamics. First, we consider the minimal CPT-odd sector, where the Lorentz violation is caused by the Carroll–Field–Jackiw (CFJ) term, namely, ∼ μ ν α β (k A F) μ A ν F α β , and we treat the Lorentz breaking parameter (k A F) μ perturbatively up to second order. We consider effects due to the presence of point-like charges, Dirac strings and point-like dipoles. In special, we calculate the electromagnetic field produced outside the string and investigate the so-called Aharonov–Bohm bound states in Lorentz violation context. Afterwards, we consider a model where the Lorentz violation is generated by the higher-derivative version of the CFJ model, namely, ∼ μ ν α β V μ A ν □ F α β , which is a dimension five term of the CPT-odd sector of the nonminimal SME. For this higher-derivative model, we obtain effects up to second order in V μ related to the presence of point-like charges and a steady current line. We use overestimated constraints for the Lorentz violation parameters in order to investigate the physical relevance of some results found in atomic systems. We also make an overestimate for the background vectors using experimental data from the atomic electric field. [ABSTRACT FROM AUTHOR]

We shall analyze the intrinsic geometric structure of Yang-Mills theory from the standpoint provided by (what we shall call) the homotopic paradigm. This mathematical paradigm was mainly developed in the framework of (higher) category theory and homotopy type theory and relies on a groupoid-theoretical understanding of equality statements of the form a ​= ​ b. From a philosophical perspective, we shall argue that the homotopic paradigm relies a) on a rejection of Leibniz's Principle of the Identity of Indiscernibles and b) on a constructivist understanding of propositions as types of proofs. We shall apply the homotopic reconceptualization of equalities to the equalities between the base points and the fibers of the fiber bundle associated to a Yang-Mills theory. We shall revisit in this framework the articulation (heuristically established in the framework of the so-called gauge argument) between gauge symmetries and the mathematical notion of connection. We shall argue that this homotopic-theoretic understanding of Yang-Mills theories paves the way toward an ontological interpretation of gauge symmetries, that is an interpretation according to which gauge symmetries—far from being nothing but a " surplus structure " resulting from a descriptive redundancy—rely on the intrinsic geometric structures of Yang-Mills theories. [ABSTRACT FROM AUTHOR]

Based on the construction of the 4‐dim noncommutative gravity model described in our previous work, first, a more extended description of the covariant noncommutative space (fuzzy 4‐dim de Sitter space), which accommodates the gravity model, is presented and then the corresponding field equations, which are obtained after variation of the previously proposed action, are extracted. Also, a spontaneous breaking of the initial symmetry is performed, this time induced by the introduction of an auxiliary scalar field, and its implications in the reduced theory, which is produced after considering the commutative limit, are examined. Based on the construction of the 4‐dim noncommutative gravity model described in previous work, first, a more extended description of the covariant noncommutative space (fuzzy 4‐dim de Sitter space), which accommodates the gravity model, is presented and then the corresponding field equations, which are obtained after variation of the previously proposed action, are extracted. Also, a spontaneous breaking of the initial symmetry is performed, this time induced by the introduction of an auxiliary scalar field, and its implications in the reduced theory, which is produced after considering the commutative limit, are examined. [ABSTRACT FROM AUTHOR]

This paper criticizes the traditional philosophical account of the quantization of gauge theories and offers an alternative. On the received view, gauge theories resist quantization because they feature distinct mathematical representatives of the same physical state of affairs. This resistance is overcome by a sequence of ad hoc modifications, justified in part by reference to semiclassical electrodynamics. Among other things, these modifications introduce "ghosts": particles with unphysical properties which do not appear in asymptotic states and which are said to be purely a notational convenience. I argue that this sequence of modifications is unjustified and inadequate, making it a poor basis for the interpretation of ghosts. I then argue that gauge theories can be quantized by the same method as any other theory. On this account, ghosts are not purely notation: they are coordinates on the classical configuration space of the theory—specifically, on its gauge structure. This interpretation does not fall prey to the standard philosophical arguments against the significance of ghosts, due to Weingard. Weingard's argumentative strategy, properly applied, in fact tells in favor of ghosts' physical significance. [ABSTRACT FROM AUTHOR]

Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of U(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an S 4 permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame-dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field. [ABSTRACT FROM AUTHOR]

We analyze the asymptotic stability of the SU(n) Dark Monopole solutions and we show that there are unstable modes associated with them. We obtain the explicit form of the unstable perturbations and the associated negative-squared eigenfrequencies.

I review here some motivations to consider a theory of gravity based on independent metric and connection, and its status as a quantum theory. [ABSTRACT FROM AUTHOR]

Symmetries in modern physics are a fundamental subject of high relevance that allows appreciating more deeply the physical structure of a theory. In this paper, we analyze a gauge symmetry that appears in complex holomorphic systems. We show that a complex system can be reduced to different real systems, using different gauge conditions, and the gauge transformations connect several real systems in the complex space. We prove that the space of solutions of one system is related using a gauge transformation to another one. Gauge transformations are, in some cases, canonical transformations. However, in other cases, these are more general transformations that change the symplectic structure, but there is still a map between systems. We establish a construction to extend the analysis to the quantum case using path integrals through the Batalin–Fradkin–Vilkovisky theorem and within the canonical formalism, where we show explicitly that solutions of the Schrödinger equation are gauge-related. [ABSTRACT FROM AUTHOR]